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'Snail Trails' printed from http://nrich.maths.org/
This is a game for two players. You will need some small-square
grid paper, a die and two felt-tip pens or highlighters.
- Mark a starting point and a target square.
- Players take turns to roll the die, then move that number of
squares in a straight line.
- Move only vertically (up/down) or horizontally (across), never
- You can cross over the other player's trails. You can trace
over the top of the other player's trails.
- You can cross over a single trail of your own, but can never
cross a pair of your trails (side-by-side) or trace over your own
- To win, you must roll the exact number needed to finish in the
target square. You can never pass through the target square.
- The game ends when a player ends his/her trail in the target
square, OR when a player cannot move without breaking any of the
Does it matter where the target is put? Is there a good strategy
for winning? If you could choose your own numbers, what would be
the shortest possible trail?